MinT - Best Known (147, 147+57, s)-Nets in Base 4

Best Known (147, 147+57, s)-Nets in Base 4

(147, 147+57, 531)-Net over F₄ — Constructive and digital

Digital (147, 204, 531)-net over F₄, using

6 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 70, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(147, 147+57, 1146)-Net over F₄ — Digital

Digital (147, 204, 1146)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+57, 87237)-Net in Base 4 — Upper bound on s

There is no (147, 204, 87238)-net in base 4, because

1 times m-reduction [i] would yield (147, 203, 87238)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 165 270736 155654 835297 540266 116226 823758 377207 435345 192302 488646 713554 096645 369978 581131 907019 330079 699732 901648 729735 086760 > 4²⁰³ [i]